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Variance of ANOVA-based estimator sˆ2M for differing sub-population sizes nk, 1 = k = K

Author

Listed:
  • Mohammed Shahid Abdulla

    (Indian Institute of Management Kozhikode)

  • L Ramprasath

    (Indian Institute of Management Kozhikode)

Abstract

Analysis of Variance (ANOVA) is a popular method to infer whethersub-populations have effects that are strong enough to reject the nullhypothesis, in the face of observation noise. The variance of conditionalexpectation (Var-of-CE) is the variance of these effects in sub-populations,and this is estimated by sampling a sub-population of sizenk, for each sub-populationk, and by samplingKsuch sub-populations. For the generalcase of varyingnk, it is unknown what the variance of this estimatoris, though it is known for the special casenk=n,n=2for allk?{1,2,...,K}as in [1]. The following derivation settles the former questionand is of value in use-cases where sampling has constraints

Suggested Citation

  • Mohammed Shahid Abdulla & L Ramprasath, 2019. "Variance of ANOVA-based estimator sˆ2M for differing sub-population sizes nk, 1 = k = K," Working papers 338, Indian Institute of Management Kozhikode.
    • Handle: RePEc:iik:wpaper:338
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